1. Field of the Invention
The present invention relates to an apparatus for hybrid multiplication, and more particularly, to an apparatus for hybrid multiplication in finite field GF(2m) capable of achieving trade-off between the area and the performance of an apparatus for multiplication.
2. Description of the Related Art
A variety of operations in GF(2m) are widely used in communications systems or public-key cryptosystems. The GF(2m) operation in communication systems is used to enhance the reliability of information and m is determined with respect to the amount of data to be guaranteed for reliability. The exponent m has close relation with the size of hardware for calculation. For communication systems, m in a range from 8 to 32 is used, and a basic calculator for this, such as an adder, a multiplier, an inverse multiplier, is relatively easily implemented.
Meanwhile, in public-key cryptosystems, m is determined according to a guaranteed security, and in case of an elliptic curve cryptosystem (ECC), in order to guarantee sufficient security, m of 160 or over is recommended. Thus, for large m, the area as well as the performance of hardware should be considered. In particular, in case of a multiplier taking a major part of public-key cryptosystem calculations, the difference between the performance and the area can increase depending on the implementation method, and consequently, the difference of the performance of the entire system can increase.
An apparatus for multiplication in GF(2m) can be designed by a bit-serial method or a bit-parallel method. The bit-serial method has an advantage of hardware implementation with a small area, but the operation should be repeatedly performed m or more times such that the operation time increases and the performance of the system can be lowered. Meanwhile, the bit-parallel method can be expected to provide a high-speed operation performance, but with increasing m, the area of the hardware increases by a factor of 2 such that in case of a large system, there is difficult in implementation.